BZOJ 4805 欧拉函数求和

Posted 2020-10-24 zzyer

题解：杜教筛

问题：式子推的不熟

#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
using namespace std;
typedef long long Lint;

int n;
map<int,Lint>f;

int cntprime;
int prime[1000009];
int vis[10000009];
Lint phi[10000009];
void Lineshake(){
	phi[1]=1;vis[1]=1;
	for(int i=2;i<=10000000;++i){
		if(!vis[i]){
			prime[++cntprime]=i;
			phi[i]=i-1;
		}
		for(int j=1;(j<=cntprime)&&(i*prime[j]<=10000000);++j){
			vis[i*prime[j]]=1;
			if(i%prime[j]==0){
				phi[i*prime[j]]=phi[i]*prime[j];
				break;
			}
			phi[i*prime[j]]=phi[i]*(prime[j]-1);
		}
	}
	for(int i=2;i<=10000000;++i)phi[i]+=phi[i-1];
}

Lint Calc(int n){
	if(n<=10000000)return phi[n];
	if(f.count(n))return f[n];
	Lint ret=n*1LL*(n+1)/2;
	int last;
	for(int d=2;d<=n;d=last+1){
		last=n/(n/d);
		ret-=(last-d+1)*Calc(n/d);
	}
	f[n]=ret;
	return ret;
}

int main(){
	scanf("%d",&n);
	Lineshake();
	cout<<Calc(n);
	return 0;
}